This tended to happen to a few Nokia phones I owned after a few years (and others but recently it's only been Nokias I've tended to hold onto for any prolonged period), but for a lot of different reasons.
The problem is with the battery, the phone is losing power and turning off. It might not technically be the battery though. I had a phone where a similiar problem arose due to the connectors (little gold bits that go from the phone to touch the battery) being damaged and another where a replacement battery, free off a friend (a good way to check if you have someone you could borrow one off for a few days), fixed the problem.
From the details it's impossible for anyone to give a definate answer on what is causing it. It could be the battery is faulty, a problem with the connections from the battery to the phone or it could be a problem with the phone itself, all we can say is that it is turning off.